Electromagnetic radiation has been very useful in a wide range of applications, such as communication, imaging, remote sensing, material processing, medical therapy, scientific investigation, etc. It is well known that radiation generation requires acceleration or deceleration (acceleration in the negative sense) of charged particles. For example, an alternating-current (AC) electric power supply may drive electrons in a radiation antenna to generate electromagnetic radiation. In prior arts, the radiation frequency from a stationary antenna is the same as the driving frequency of the power supply, while the radiation frequency depending on the moving speed of an electric pulse in an antenna has never been considered.
Radiation can also be generated from the acceleration of a moving charge in vacuum. When a radiation source moves relative to a radiation detector, the detected radiation frequency is shifted by an amount depending on the direction and speed of the radiation source. To generate a short-wavelength radiation, one may take advantage of the strong frequency up-shift of the radiation from a transversely accelerated charged particle moving longitudinally toward a radiation detector at nearly the speed of light. When an object moves near the speed of light, called a relativistic object, its physics is governed by the theory of relativity. Whether a moving object is in the relativistic regime is usually characterized by the so-called Lorentz factor, given by γ=1√{square root over (1−β2)}, where β=v/c with v the speed of the particle and c the speed of light in vacuum. A relativistic object moves near the speed of light v˜c, having a Lorentz factor γ>>1. The radiation generated from a relativistic charged particle is known as “relativistic radiation”. The frequency of relativistic radiation is characterized by two important effects, Lorentz contraction and relativistic Doppler shift. The former is a contraction of a spatial length in the moving object's frame according to the theory of special relativity. The later is the usual Doppler shift corrected by the theory of the special relativity when a radiation source moves near the speed of light. Both effects greatly shorten the radiation wavelength at a detector when a radiation source moves toward the detector. Another characteristic of relativistic radiation is its radiation power strongly depending on the speed of the radiation source. A near-speed-of-light radiation source can follow closely the generated speed-of-light radiation field, leading to concentration of the radiation energy in a short temporal duration or high power. Relativistic radiation has covered a wide spectral range from microwave to x-ray. Notable relativistic radiations include undulator radiation, synchrotron radiation, free-electron laser, Smith-Purcell radiation, Cherenkov radiation, backward-wave oscillation, transition radiation, diffraction radiation, and so on.
As a first example of relativistic radiation, synchrotron radiation is generated when a relativistic charged particle, usually an electron, is bent by a magnetic field. The high-frequency cutoff of synchrotron radiation is expressed by
                              f          c                =                                            3              ⁢                                                          ⁢                              γ                3                                                    2              ⁢                                                          ⁢              π                                ⁢                      (                          c              ρ                        )                                              (        1        )            where ρ is the bending radius of curvature of the charge's trajectory. As can be seen from (1), the radiation spectrum is broadband, extending into the valuable VUV and soft x-ray wavelengths for a highly relativistic electron with GeV energy (γ˜2000 for 1-GeV electron).
As a second example, narrow-band undulator radiation is generated from relativistic electrons traversing a magnetic structure, called an undulator, in which an alternating transverse magnetic field forces axially moving electrons to perform a quiver motion and emit a radiation in the axial direction. Assume the undulator axis is along z. From the theory of special relativity the undulator period λu in the electron moving frame is contracted by a Lorentz factor (Lorentz contraction), given λu/γz, where γz−1/√{square root over (1−βz2)}=1√{square root over (1−(β2−β⊥2))} is the longitudinal Lorentz factor with βz= vz/c being the average longitudinal speed of the electron vz normalized to the speed of light c and β⊥ being the transverse component of the β factor. The oscillation frequency of the electrons in the electron rest frame is therefore f′=(λu/(γzvz)−1. Owing to the relativistic Doppler shift, the radiation frequency detected in the laboratory frame along z is shifted by a factor √{square root over ((1+βz)/(1−βz))}{square root over ((1+βz)/(1−βz))}, resulting in the well known expression for the undulator-radiation wavelength in the axial direction:
                              λ          r                =                                            λ              u                        ⁡                          (                                                c                                                            v                      _                                        z                                                  -                1                            )                                =                                                    λ                u                            ⁡                              (                                                      1                                          β                      z                                                        -                  1                                )                                      .                                              (        2        )            In the relativistic limit vz˜c and γz>>1, Eq. (2) reduces to λr˜λu/2γz2. For vz˜c to be valid, the electron's quiver motion has to be small or β⊥<<1. In this limit, βz˜β and γz˜γ for a relativistic electron. Therefore, the radiation wavelength λr from a relativistic electron can be a small fraction of the undulator wavelength λu. This relativistic mechanism helps to generate valuable short-wavelength radiation for a variety of applications.
In relativistic radiation, the radiation is usually generated from a group of relativistic electrons of a certain temporal length, called an electron pulse. When the electron pulse length is much smaller than the radiation wavelength, all the electrons radiate coherently at nearly the same phase of the electromagnetic field. The radiation energy for such coherent radiation is proportional to the square of the radiation field, having a value proportional to the square of the total charge participating in the radiation. On the other hand, when the electron pulse length is significantly longer than the radiation wavelength, electrons located at different radiation phases emit radiation incoherently and give a total radiation energy linearly proportional to the total charge participating in the radiation. Apparently coherent radiation can be much more powerful than incoherent radiation due to the quadratic dependence of the radiation energy on the radiating charge.
The spectral energy of relativistic radiation, radiation energy per unit radiation bandwidth, can be greatly improved when a periodic electron-pulse train transverses a radiation device. The radiation field is coherently and constructively added at the frequency or the harmonics of the frequency of the electron pulses. For example, the fractional radiation line width from N periodic electron pulses is 1/N, which can be a very small value for a large N.
In prior arts, the near-speed-of-light charged particles, usually electrons, are prepared by a large-size and expensive particle accelerator system. The radiation device, such as the undulator or a bending magnet, is also very bulky, heavy, and expensive. Furthermore, dumping relativistic charged particles after an application imposes serious x-ray and pray radiation hazard to a user or an operator of relativistic radiation apparatus. Consequently, most relativistic radiation is only available in a national-scale user facility having careful and extensive radiation shielding.
The first valuable insight of the present invention is to recognize that a density wave of charges or an alternating electric signal in a conducting wire can propagate at nearly the speed of light and can radiate from a properly designed antenna. Usually, an antenna wire carrying an electric signal with positive and negative cycles, containing no net charge when being averaged over the whole wire or a cycle of the signal oscillation. As a second valuable insight of the present invention, if one could create a current pulse carrying a net charge on a conducting wire, the current pulse or a pulsed charge wave will propagate near the speed of light along the wire just like a pulse of real relativistic charges propagating in free space. The net-charge pulse does not possess a mass and is therefore termed as a “quasi charged particle” in the present invention. The relativistic-like radiation generated from a quasi charged particle moving near the speed of light is termed as “quasi relativistic radiation” for what follows.
In principle, quasi relativistic radiations from positive and negative quasi charged particles differ only in the polarity of the radiation field. In practice, it is easier to generate a positive quasi charged particle, effectively void of electrons, by knocking out a short group of electrons from a conducting wire. This positive quasi charged particle can propagate nearly the speed of light on the wire just like a positive relativistic charged particle, a positron or proton pulse, propagating in vacuum. As a scheme of the present invention, a short-pulse laser knocks out electrons from an antenna wire by virtue of photoemission to create such a near-speed-of-light positive quasi charged particle to propagate along a structured antenna wire to emit the quasi relativistic radiation. To an observer measuring radiation, the radiation generated by a quasi charged particle without a mass has no difference from that generated by a real charged particle with a mass, as long as both the particles carry the same amount of charge and move along the same trajectory with the same speed. From the theory of electrodynamics, mass is simply not in the equation of calculating the radiation generated by a charge. As an embodiment of the present invention, undulator-like radiation can be generated by exciting a quasi charged particle on an antenna wire with the shape of the wire mimicking the trajectory of a relativistic charge in an undulator; synchrotron-like radiation can be generated by exciting a quasi charged particle on an antenna wire with the wire bent with a curvature mimicking the trajectory of a relativistic charge traversing a bending magnet; diffraction radiation can be generated by exciting a quasi charged particle on an antenna wire with the wire and thus the quasi charged particle transmitting through an aperture. Another embodiment of the present invention is to simply insert a straight conducting wire carrying a quasi charged particle to the axis of an undulator, in which the quasi charged particle performs a small amplitude quiver motion on the wire, while propagating down the straight wire on the undulator axis, to emit undulator-like radiation with a much reduced radiation wavelength in the limit of γz approaching γ. Similar embodiments of the present invention are a Smith-Purcell grating, a traveling-wave tube, and a backward-wave oscillator with their axes arranged with a conducting wire carrying a quasi charged particle. The present invention does not have the complexity of an expensive particle accelerator system and avoids the inconvenience of operating a relativistic-radiation machine in a radiation shielded area. All the aforementioned and additional embodiments of the present invention will be further defined below.
The present invention has apparent advantages over the prior arts in reducing the cost and complexity for generating the relativistic radiation. It is therefore the intention of the present invention to disclose a new scheme and apparatus of generating relativistic radiation to overcome the aforementioned drawbacks in the prior arts.